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Derivative of:
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Graphing y =:
x^3-e^-x
Identical expressions
x^ three -e^-x
x cubed minus e to the power of minus x
x to the power of three minus e to the power of minus x
x3-e-x
x³-e^-x
x to the power of 3-e to the power of -x
Similar expressions
x^3+e^-x
x^3-e^+x

The derivative of the function/ x^3-e^-x

Derivative of x^3-e^-x

The solution

You have entered [src]

 3    -x
x  - e

$$x^{3} - e^{- x}$$

d / 3    -x\
--\x  - e  /
dx

$$\frac{d}{d x} \left(x^{3} - e^{- x}\right)$$

Transform

Detail solution

Differentiate $x^{3} - e^{- x}$ term by term:
1. Apply the power rule: $x^{3}$ goes to $3 x^{2}$
2. The derivative of a constant times a function is the constant times the derivative of the function.
  1. Let $u = - x$ .
  2. The derivative of $e^{u}$ is itself.
  3. Then, apply the chain rule. Multiply by $\frac{d}{d x} \left(- x\right)$ :
    1. The derivative of a constant times a function is the constant times the derivative of the function.
      1. Apply the power rule: $x$ goes to $1$
      So, the result is: $-1$
    The result of the chain rule is:
    
    $- e^{- x}$
  So, the result is: $e^{- x}$
The result is: $3 x^{2} + e^{- x}$

The answer is:

$3 x^{2} + e^{- x}$

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

   2    -x
3*x  + e

$$3 x^{2} + e^{- x}$$

Simplify

The second derivative [src]

   -x      
- e   + 6*x

$$6 x - e^{- x}$$

Simplify

The third derivative [src]

     -x
6 + e

$$6 + e^{- x}$$

Simplify

The graph

Derivative of x^3-e^-x